IOT devices are expected to drive many useful applications

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1 1 Energy Effiient Barring Fator Enabled Extended Aess Barring for IoT Devies in LTE-Advaned Prashant K.Wali and Debabrata Das, Senior Member, IEEE arxiv: v1 [s.ni] 9 Nov 216 Abstrat Synhronized Random Aess Channel RACH attempts by Internet of Things IoT devies ould result in Radio Aess Network RAN overload in LTE-A. 3GPP adopted Barring Bitmap Enabled-Extended Aess Barring EAB-BB mehanism that announes the EAB information i.e., a list of barred Aess Classes through a barring bitmap as the baseline solution to mitigate the RAN overload. EAB-BB was analyzed for its optimal performane in a reent work. However, there has been no work that analyzes Barring Fator Enabled- Extended Aess Barring EAB-BF, an alternative mehanism that was onsidered during the standardization proess. Due to the modeling omplexity involved, not only has it been diffiult to analyze EAB-BF, but also, a muh more far-reahing issue, like the effet of these shemes on key network performane parameter, like enodeb energy onsumption, has been overlooked. In this regard, for the first time, we develop a novel analytial model for EAB-BF to obtain its performane metris. Results obtained from our analysis and simulation are seen to math very well. Furthermore, we also build an enodeb energy onsumption model to serve the IoT RACH requests. We then show that our analytial and energy onsumption models an be ombined to obtain EAB-BF settings that an minimize enodeb energy onsumption, while simultaneously providing optimal Quality of Servie QoS performane. Results obtained reveal that the optimal performane of EAB-BF is better than that of EAB-BB. Furthermore, we also show that not only all the three 3GPPproposed EAB-BF settings onsidered during standardization provide sub-optimal QoS to devies, but also result in exessive enodeb energy onsumption, thereby autely penalizing the network. Finally, we provide orretions to these 3GPP-settings that an lead to signifiant gains in EAB-BF performane. Index Terms Extended Aess Barring, Green Communiations, Internet of Things, IoT Aess, LTE-Advaned, RAN Overload. I. INTRODUCTION IOT devies are expeted to drive many useful appliations like smart grids and asset traking [1]. These appliations require the devies to report their data periodially to a remote server. Hene, there is a need for an infrastruture to provide them aess to the bakbone network. LTE-A is seen as a solution for this beause of its salient features like high data rates, low lateny, support for large bandwidth [2] and good overage. However, sine these IoT devies report data periodially with an interval of the order of a few minutes to a day [3], [4], they lose uplink synhronization with the Manusript reeived Otober 26, 216. This work was supported by a projet funded by DeitY, Govt. of India. Prashant Wali is with International Institute of Information Tehnology- Bangalore, Bangalore 561, India iwalihere@gmail.om Debabrata Das is with International Institute of Information Tehnology- Bangalore, Bangalore 561, India ddas@iiitb.a.in enodeb between eah aess 1 whih an only be regained by ompleting the RACH proedure. But, for a ertain lass of devies like the smart meters, a large number of them making RACH attempts within a very short period of time results in many preamble ollisions. This leads to RAN overload [2] severely affeting the QoS suess probability, network aess delay of the devies. To mitigate the RAN overload, several tehniques see for instane [2], [4], [6], [7], [8] and the referenes therein have been proposed among whih 3GPP onsidered Extended Aess Barring EAB as the baseline solution. Two alternative barring mehanisms were onsidered for EAB onfigured devies [9]. The first method is based on dividing the devies into 1 Aess Classes ACs and applying the ON/OFF priniple per AC -9. With this approah, all devies with EAB onfigured are either barred or not barred from making RACH attempts depending on their AC. System information update is required to end barring for the prohibited devie lasses or to hange the barred lasses. In order to allow all EAB devies to aess the network at some point of time, the aess opportunities need to be irulated between ACs [9]. In our work, we all this method as Bitmap Barring Enabled-EAB and refer to it as EAB-BB. The seond method is based on a probability value barring fator and a timer bakoff timer. In this method, devies that are onfigured with EAB would generate a random number between and 1 prior to performing RACH. If the random number is lower than the barring fator, the EAB test is passed and devies may attempt RACH. Otherwise, they have to wait a given amount of time indiated by the bakoff timer and draw a new random number before attempting RACH again. The Probability based barring was onsidered by proposing three settings EAB.5,16s, EAB.7, 8 s and EAB.9, 4 s during the standardization proess [3], [4]. In our work, we all this method as Barring Fator Enabled-EAB and refer to it as EAB-BF 2. EAB-BB was adopted by 3GPP [9] and was analyzed for its optimal performane in a reent work [9]. However, there has been no work that investigates the optimal performane of EAB-BF. Hene, to the best of our knowledge, it is not known whether EAB-BB has the best performane among these two methods that were onsidered to enable EAB. Moreover in 1 The devie loses uplink synhronization if it does not ommuniate with the LTE-A base station alled as enodeb for 1-2 seonds sine the enodeb UE-INACTIVITY-TIMER expires [5]. 2 Note that EAB-BF was alled EAB [4] before EAB-BB was also onsidered as an alternative method and adopted by 3GPP with the same name. Hene we introdue the two names EAB-BF and EAB-BB in order to distinguish the two mehanisms from eah other.

2 2 pratie, for EAB-BB the system information needs to be updated whih is ostly both for UEs and the network. Also, the barred/unbarred approah may reate peaks to RACH load when the broadasted aess information hanges, i.e., when barring is ended, a burst of aesses may our. In [1], the authors based on their analysis show that long paging yle limits the performane of the barring phase and short paging yle limits the performane of the release phase of EAB-BB. Hene, any QoS that requires either a long or a short paging yle might lead to the aforementioned problems. Also, in [9], the authors adopt an algorithm to let the enodeb to turn EAB on or off aording to a ongestion oeffiient. But it is not lear how the hoie of the ongestion oeffiient threshold value affets transmission periods of SIB14 and the paging yle and in turn the suess probability and mean aess delay in general. Beause of the aforementioned reasons, there is a need to investigate and ompare the optimal performane of EAB-BB with that of EAB-BF that an avoid its operational omplexities. Additionally, there is also an urgent need to investigate an equally important issue of minimizing the enodeb energy onsumption while ensuring optimal performane. Minimizing the enodeb energy onsumption will have far-reahing benefits beause of the following reasons: i the enormous growth in the ellular industry has already pushed the limits of energy onsumption resulting in tens of Mega-Joules of energy being onsumed annually, ii IoT devies have very little data to report in eah aess, so there is a need to keep the enodeb energy onsumption at minimum while serving them and iii enodebs are the largest energy onsumers in a ellular network, taking 6% of the total share [11], so any redution in their energy onsumption will have a substantial bearing on the total network energy onsumption. Previous works that investigate methods to redue enodeb energy onsumption onsider only downlink data traffi see for instane [12], [13], [14], [15] in the absene of IoT devies. Works like [16], whih inlude energy onsumption of IoT devies along with their onventional performane metris, help extend the life of IoT devies but not in saling down the energy onsumption of a ellular network. Note that the primary purpose of RAN overload ontrol is to relieve the RACH ongestion. But it should not stop us from onsidering an important aspet like saving energy if we an ahieve it simultaneously along with RAN overload ontrol. Even though the major power onsumption is believed to result from traditional voie/data servies, there an be time intervals when this traffi is low to very low. It is known that the traffi in real ellular networks an be modeled as having a periodi sinusoidal profile indiating a large portion of time when the traffi is quite low [17]. This, added to the fat that these IoT devies ontinuously make periodi RACH attempts lasting at least 15-2 seonds with a periodiity that ould get as low as 5 minutes [2] irrespetive of other traffi, means that over large frations of time, the enodeb spends onsiderable energy serving these IoT devies. This entails us to investigate if the enodeb energy onsumption an be minimized while effeting RAN overload ontrol without ompromising on the desired QoS of IoT devies. Hene, this work onentrates only on those intervals when the traditional voie/data traffi is very low or non-existent. Nevertheless, as a future work, our urrent analysis an be extended to intervals that have high voie/data traffi by looking at the number of extra subframes required to shedule the downlink traffi after dediating some for handling the RACH attempts of the IoT devies. Note that even though the energy saving per aess yle in this ase ould be lesser ompared to intervals when the traditional traffi is non existent, the fat that these devies are periodially required to lear RACH, amounts to a huge energy saving in the long run onsidering around 4 million base stations aross the globe [11]. Inspite the signifiant benefits mentioned above, to the best of our knowledge, there have not been any works that have either attempted to find the optimal performane of EAB-BF alone or along with simultaneously minimizing the enodeb energy onsumption. Although EAB-BF has been analyzed in [4], it was done only to investigate the performane of the three 3GPP settings that were onsidered during the standardization proess and not to find the settings that ensure its optimal performane. Also, an important element missing in their analysis is the mean aess delay. In our work, we derive exat losed expressions for the expeted number of devies that attempt and ollide in eah RACH slot when EAB-BF is employed. We then use these expressions to obtain the suess probability and the mean aess delay for an attempting devie. This kind of an analysis allows us to aurately apture the dynamis in eah RACH slot and also mathematially show how the suess probability and the mean aess delay depend on expeted number of devies that attempt and ollide, along with EAB-BF parameters. We next build a model for the energy onsumed by the enodeb to serve the IoT devies RACH requests. Combining the aforementioned losed form expressions with the energy onsumption model of the enodeb then helps obtain EAB-BF settings, that an simultaneously minimize enodeb energy onsumption, maximize suess probability and minimize mean aess delay for IoT devies while satisfying a given QoS onstraint. Simulation results for various EAB- BF settings show that the losed form expressions obtained through our analysis yield aurate results. Our work an be termed novel and gains signifiant importane beause of the kind of ontributions it allows us to make. Speifially, our ontributions are summarized as follows. 1 We present a novel analytial model to obtain the suess probability and the mean aess delay of the IoT devies under the influene of EAB-BF. We also build an energy onsumption model of the enodeb to serve the IoT devies RACH requests. 2 We next illustrate how to ombine our analytial model of EAB-BF with enodeb energy onsumption model, to obtain optimal EAB-BF settings, i.e, the barring parameters, that minimize the enodeb energy onsumption while simultaneously providing desired QoS to IoT devies during the RACH proedure. Speifially, we illustrate how our analytial expressions an help in building searh algorithms to obtain these optimal settings, through an

3 3 TABLE I SUMMARY OF THE SYMBOLS USED Symbol Parameter Typial Value used in simulations N Total number of IoT devies in the ell 3 K Number of preambles 54 W Bakoff Window interval after ollision in 2 ms mse r p Rah periodiity in mse 5 ms P eab EAB Barring Probability.5,.7 and.9 T eab EAB Bakoff Time 16 s, 8 s and 4 s Fig. 1. System Model for RACH Slots and New Arrivals II. SYSTEM MODEL example. To that end, this work ould also perhaps motivate newer searh algorithms if required. 3 Using the results obtained from the example searh algorithm that we present, the optimal performane of EAB- BF is shown to be better than that of EAB-BB whih is onsidered state of the art. This indiates that EAB-BB may not be the best hoie to handle densely populated IoT devies in its urrent form or requires further researh to improve its performane. 4 Our results also reveal that all the three 3GPP-proposed settings for EAB-BF onsidered during standardization not only provide sub-optimal QoS to devies, but also result in exessive enodeb energy onsumption, thereby autely penalizing the network. Our study then shows that orretions an be made to these 3GPP settings so that the energy onsumed by the enodeb and the mean aess delay an be redued by 5% with more than 5% gain in suess probability ompared to one of the three 3GPP settings. A 5% redution in energy onsumption along with a substantial redution in aess delay an be obtained against the other two 3GPP settings without any degradation in the suess probability. This is in ontrast to the general belief that a gain in suess probability an be ahieved only at the ost of mean aess delay or vie-versa. In this regard, a key insight that our work provides is that a derease in mean aess delay is possible either with an inrease or without any derease in suess probability if we move from a suboptimal performane point to an optimal performane point or in other words, if we modify a sub-optimal setting to make it an optimal setting. The rest of the paper is organized as follows. The system model is developed in Setion II. In Setion III, we develop the LTE-A enodeb energy onsumption model to serve IoT devies RACH requests. In Setion IV, we define the performane metris whih motivates the analysis of EAB- BF. The joint optimization of EAB-BF and enodeb energy onsumption is investigated in Setion V in whih we also present an example searh algorithm that an be built from our analytial expressions to obtain the optimal performane of EAB-BF. Results obtained from this algorithm are then used to ompare with the performane of EAB-BB and the 3GPP proposed EAB-BF settings. Setion VI onludes the paper. We onsider a set of IoT devies already registered with the enodeb. The devies get ativated periodially and try to aess the network to send data. The periodiity an range from a few minutes to a few hours or days [2]. We assume that eah aess period alled as yle heneforth begins at time t = for simpliity. Sine a devie is inative for at least a few minutes between eah network aess, it gets detahed from its serving enodeb. Hene, eah devie tries to re-establish uplink synhronization with the enodeb through the RACH proedure in every yle, after it gets ativated at time t T A aording to a density funtion pt. The density funtion pt ould be derived from a trunated beta distribution speified by 3GPP [2] as follows, pt = tα 1 T A t β 1 T α+β 1 A Betaα,β, 1 where, α,β > and Betaα,β is the Beta funtion. Denoting the total number of IoT devies in the ell by N, the aess intensity λ i of the IoT devies is given by [2], λ i = N ti t i 1 ptdt, 2 where, t i is the time of the i th RACH slot within that aess yle. We assume that within the ativation time T A, there are M RACH slots as shown in Fig. 1. The RACH periodiity whih is the length of the interval between two suessive RACH slots is denoted by r p. Let the interval [t i 1,t i 1 +r p ] = [t i 1,t i ] be alled interval i. All the devies that get ativated in the interval i are onsidered as new arrivals for the i th RACH slot. Note that all the devies get ativated within time T A, and for t > T A, devies that experiene ollisions an re-attempt the RACH proedure. EAB-BF is denoted by EABP eab,t eab. For larity, we use EAB-BF to indiate the EAB mehanism that employs the barring fator method and EAB test to indiate the barring test that a devie takes by generating a random number, to be allowed to make a RACH attempt. As explained in the previous setion, whenever a devie fails in the EAB test by generating a number larger than P eab, it baks off for a fixed time T eab seonds and repeats this proedure until a

4 4 number smaller than P eab is hosen [4] 3. If the devie passes the EAB test by generating a number less than P eab, it is allowed to start the RACH proedure by sending a preamble to the enodeb after hoosing it randomly from a set of 54 sequenes. A ollision ours when two or more devies hoose same preamble sequenes resulting in RACH failure 4. If the preamble ollides, the devie baks off for a time that is uniformly distributed over [,W 1] ms and again performs EAB test after returning from bakoff. It follows this proedure after eah ollision. On the other hand, if the preamble does not ollide, then, we assume that the preamble is deteted by the enodeb 5, in whih ase, the enodeb aknowledges with a Random Aess Response RAR message within the RAR window RAR window is a set of subframes in the downlink in whih the enodeb sends the RAR messages. The RAR message is used to send the timing advane information, uplink resoure grant for message 3 to be sent by the UE and temporary identify the UE among other things. After some RAR proessing time, the devie transmits Radio Resoure Control RRC onnetion request message via the Physial Uplink Shared Channel PUSCH using the resoures granted by RAR. As enodeb needs to establish whih devie sent whih preamble, ollision resolution proess is required. The RACH proedure ends with a suessful reeption of RRC onnetion set-up message from enodeb. We assume that both T eab and W are integer multiples of the RACH periodiity r p for simpliity. Depending on the QoS requirement of the devies, the enodeb has to deide the optimal settings of EAB-BF, i.e., Peab and T eab, that provide the desired QoS with minimum enodeb energy onsumption. To make this deision, the enodeb holds a database whih an be reated offline by the network operator and uploaded into enodeb as indiated even in [9] or an be reated by the enodeb itself of the minimum energy onsuming settings for eah of the possible QoS requirements of the IoT devies. The enodeb an know about the QoS requirement of devies during registration through the establishment ause information in RRC Connetion Request Message sent by the devies during the initial RACH proedure [2]. The enodeb then has to ommuniate optimal barring parameters pair Peab,T eab one to devies, unlike EAB-BB, in whih the system information needs to be updated even within an aess yle when the devies are attempting RACH whih is ostly both for UEs and the enodeb. 3 Note that in another mehanism alled as Aess Class Barring ACB also, the devie generates a random number between and 1 and baks off if the generated number is greater than the barring probability, but the bak off time is random [18] and hene is different from EAB-BF. Moreover, sine our goal in this work is to analyze the optimal performane of EAB-BF [4] and ompare it with EAB-BB [9] whih was adopted by 3GPP over EAB-BF, we onsider a fixed bak off time as suggested in [4]. To the best of our knowledge, this is the first work whih derives the optimal performane of EAB-BF and ompares with that of EAB-BB. 4 This is a onservative assumption as a UE with muh stronger signal than others may be seleted even in the event of ollision due to the apture effet. But we ignore this possibility in our work. 5 There is a hane of the preamble not being deteted even when there is no ollision, albiet, with a very low probability in LTE-A sine the random aess preambles in LTE-A are normally orthogonal to other uplink transmissions [19, Setion ]. Hene we ignore this event. Even though the optimal barring parameters pair Peab,T eab have to be reomputed whenever the number of IoT devies N hanges in the ell, note that in the urrent ontext, the devies are either expeted to be deployed by the network operator or their ount is assumed to be known and remain unhanged [2]. Similar assumption is also made in [9], wherein, the authors provide optimal values of transmission periods for SIB14 messages and paging yle for a set of N devies. The devie ount being stati is justified by the fat that the number of devies do not hange frequently, and might also be regulated by the operator. In suh a senario, then, we an assume that the new optimal settings ould be obtained by the presented algorithm before the next aess yle of the devies begins, sine its periodiity is at least few minutes. Alternatively, the operator ould bar the new devies from aessing the network till a new set of optimal settings are obtained for the updated N. In either ase, the maximum ount for the devies within a single LTE-A ell is urrently speified to be 3, as per the 3GPP speifiations [2] and hene the time taken for the searh an be well within the aeptable bounds. In view of the above arguments, the algorithm presented in this work ould be either used to reate the database offline and fed into the enodeb or ould run in the enodeb itself without proving to be too ostly. Also, EAB-BF does not enounter the problem of some QoS requirements limiting its performane unlike EAB-BB, in whih if those QoS requirements demanded a long or short paging yle ould limit the performane of the barring phase and release phase. Overall, the main goal and signifiane of our work lies in building a novel analytial framework to obtain the performane metris of EAB-BF and then exhibiting a way to build searh algorithms using these performane metris, to obtain its optimal settings, whih has been illustrated through an example algorithm. Additionally, the algorithm presented in this paper also explains how the near-optimal performane values and settings of EAB-BF were obtained in our work. In this regard, this work ould perhaps motivate newer searh algorithms if required. Equally important is its ontribution in being able to help us ompare EAB-BF with EAB-BB, and showase its superior performane. III. ENODEB ENERGY CONSUMPTION TO SERVE IOT RACH REQUESTS Note that in LTE-A, if a preamble is suessfully transmitted, the atual data will then be transmitted without ontention on Physial Uplink Shared Channel PUSCH via sheduled transmissions and the time it takes is fixed [6]. Therefore, the time taken or mean number of attempts required for all the IoT devies to suessfully transmit Step 1 preamble sequenes during RACH is the dominant part ontributing to the QoS provided to IoT devies. Hene, we onentrate on the performane only during the first step of the RACH proedure. Therefore, RAR messages that use PDSCH Physial Downlink Shared Channel resoures in the downlink subframes and transmitted in response to preamble transmissions by the devies are identified as energy onsuming events.

5 5 TABLE II SUMMARY OF THE SYMBOLS USED. TYPICAL VALUES USED IF ANY ARE SHOWN IN BRACKETS. Symbol Parameters represented and Typial Values used B Bandwidth of the LTE-A ell 5 MHz M s Modulation and Coding Sheme MCS used to transmit RAR messages.93 L b Number of physial bits required to transmit one RAR message 61 D s Number of symbols in a PRB that an arry data bits 12 Nrar prb Number of RAR messages that an be inluded in one PRB 4 N prb Number of PRBs available in a subframe 25 Nmax rar Maximum number of RAR messages that an be sent in one subframe 39 N sf Number of subframes required to send r RAR messages W rar Size of the RAR window 5 subframes P o Fixed power onsumption part of enodeb 17 W P t Power transmitted per PRB.8 W δ Power Amplifier Effiieny 3% E k Energy onsumed to transmit data on k PRBs Ein r Energy onsumed to send r RAR messages In this setion, we will first provide a brief bakground of LTE-A downlink physial layer struture. We will then point to a set of 3GPP speifiations to derive an exat expression for maximum number of RAR messages that an be sent in eah subframe of the RAR window. Next, we use this model to evaluate the energy onsumed by the enodeb when the IoT devies make RACH attempts in a yle. The notations used and their meaning are summarized in Table II. A. PRB Requirement for RAR Messages in LTE-A In LTE-A, eah downlink frame is of 1 ms duration and onsists of ten subframes. Eah subframe is of 1 ms duration. A subframe onsists of two.5 ms slots, with eah slot ontaining seven OFDM symbols. In the frequeny domain, the system bandwidth B is divided into several subarriers, eah with a bandwidth of 15 khz. A set of 12 onseutive subarriers for a duration of 1 slot is alled a Physial Resoure Blok PRB. The total amount of available PRBs during one subframe depends on the number of subarriers, i.e., the total bandwidth alloated for the LTE-A arrier. For example, 1 MHz ell bandwidth would orrespond to 6 subarriers and 1 PRBs in eah subframe. In LTE-A, data is transmitted over a pair of PRBs in time domain alled as Transmission Time Interval TTI. Although all the PRBs available in the total bandwidth an be alloated for sending RAR messages in eah subframe within the RAR window, the following onstraints are imposed for the transmission of RAR messages: 1 Only QPSK modulation is allowed for RAR messages and the effetive hannel ode rate determines the number of information bits being transmitted [21]. There are tables [21, Tables , and ] that map the effetive hannel ode rate to the number of RAR information bits being transmitted. 2 Irrespetive of the bandwidth, a maximum of 2216 RAR information bits an be transmitted in a single subframe within the RAR window [22]. 3 The effetive hannel ode rate hosen should ensure that the effiieny, i.e., the RAR information bits per symbol.93 [21]. Eah RAR message requires 7 bytes, i.e., 56 bits 1 for the MAC subheader and 6 for the atual RAR message [23, Setion 6.1.5]. There an be an optional additional byte ontaining a bakoff indiator for all RARs. Let M s denote the effetive hannel ode rate hosen. Assuming that the RAR messages are sent only to the devies whose preambles were suessfully deteted i.e., no Bakoff Indiator is inluded in RAR message, the number of physial bits L b required to transmit one RAR message is equal to 56/M s bits, where,. denotes the eil funtion. Let the number of symbols in a PRB that arry data bits be denoted by D s. Then Nrar, prb whih denotes the number of RAR messages that an be inluded in one PRB, will be equal to 2D s M s /56, sine QPSK is used. The number of PRBs, i.e., N prb, in a subframe is equal to BM Hz/18kHz. Hene, denoting the maximum number of RAR messages that an be sent in one subframe by Nmax, rar the following relation holds, max = min 2Ds M s N prb,39, 3 56 N rar sine, the maximum number of RAR messages that an be onstruted with 2216 bits is equal to B. Energy Consumption Model for RAR Messages A well-aepted model of the energy onsumption in a typial LTE-A enodeb is provided in [12], [14]. The energy onsumption of a enodeb inreases linearly with the utilization of the power amplifier no. of PRB pairs on whih data is sheduled in the downlink. Sine a TTI lasts for 1 ms in LTE-A, the energy onsumed to transmit data on k PRB pairs in a TTI an be omputed as follows [12], [14]: E k = P o +kδp t 1 3 J, 4 where, δ is the power amplifier effiieny and P t is the power transmitted per PRB and P o is a onstant power fator signifying a fixed power onsumption part of the power amplifier. Sine the enodeb praties Adaptive Modulation and Coding in LTE-A, we assume that the power transmitted per PRB is fixed and equal to P t. In order to investigate the energy onsumed by the enodeb in serving the IoT devies RACH requests, we need to onsider the downlink transmissions made by the enodeb to serve the devies RACH requests whih inludes all the RAR messages sent in response to suessful preamble transmissions. Now, if preambles from r devies are suessful in a RACH slot, then the number of subframes it takes to send RAR messages to all the suessful devies would be given by: N sf = r N rar max. 5

6 6 Symbol F i Γ i A i Γ i S i C i Υ i TABLE III SUMMARY OF THE SYMBOLS USED. Parameters Number of devies ativated in the interval i Total number of devies new and retransmissions that arrive in RACH slot i Number of devies that pass the EAB test and make a preamble transmission in RACH slot i Number of devies whih fail in the EAB test in RACH slot i Number of devies that are suessful in their preamble transmission in slot i Number of devies that ollide in slot i Number of devies suessful in preamble transmission till slot i Denoting the size of the RAR window by W rar, we an then express the energy onsumed in joules by the enodeb to send RAR messages to these r suessful devies, i.e., E r in, as, minn sf,w rar Ein r minr j 1Nrar = P o + max,nmax rar 56 αp t D j=1 sm s 6 In 6, the upper limit in the summation indiates that the number of subframes used to send RAR messages annot exeed the RAR window size W rar. Therefore, if r is large enough for N sf to exeed W rar, only as many RAR messages are sent as an be inluded in W rar subframes of the RAR window. The rest of the devies will bak off assuming their preambles ollided and return bak to attempt again. The term within the summation gives the energy onsumed in eah subframe whih depends on the number of RAR messages sent. The term r j 1Nmax rar indiates the number of devies that are yet to reeive RAR messages in the j th subframe within the RAR window. Hene, the term minr j 1Nmax,N rar max rar points out that the number of devies whih reeive the RAR messages in the j th subframe of the RAR window is r j 1Nmax rar if r j 1Nrar max < Nmax, rar else the number is limited to Nmax. rar IV. PERFORMANCE METRICS AND ANALYSIS OF EAB-BF Having obtained the energy onsumption model of the enodeb for RAR messages, we now analyze EAB-BF to optimize its settings so that minimum enodeb energy is onsumed to provide the desired QoS Suess Probability and Mean Aess Delay to the devies. For a random variable X, we use E[X] and X interhangeably throughout this paper to denote the mean of X. The probability of an event A is denoted by PA. Similarly, the onditional expetion of X given A is denoted by E[X A] and PB A denotes the onditional probability of B given A. The following notations are used and summarized in Table III. Let F i represent the number of devies ativated in the interval i. Then E[F i ] represents the aess intensity given by 2. Let Γ i denote the total number of devies new and ollided that arrive in slot i to make RACH attempts. Out of Γ i that arrive, the number of devies that pass the EAB test and make a preamble transmission in the i th slot be denoted by A i. Let Γ i denote the number of devies that fail in the EAB test in slot i and bak off for time T eab. Out of the A i that attempt, let S i denote the number of devies that sueed in the i th slot while C i denotes the number of devies that ollide in slot i. Let Υ i denote the number of devies that have leared RACH suessfully till slot i. A. Performane Metris In essene, if we an obtain the expeted number of RACH attempts E[A i ] and ollisions E[C i ] for slot i, and the expeted number of suesses E[Υ i ] till slot i, then with N devies in the ell, the ollision probability denoted by P C, suess probability denoted by P S and the mean of the aess delay denoted by T AD an be obtained as follows [?]: 1 Suess Probability and Mean Number of Attempts: A devie makes a preamble transmission on passing the EAB test and beause we have assumed that a non-olliding preamble implies suessful RACH ompletion, the preamble suess probability denoted by P S an be obtained as: E[C i ] P S = 1 P C = 1 i:e[υ i]<n i:e[υ i]<n E[A i ]. 7 Sine eah RACH attempt is independent for a devie, the number of attempts to lear the RACH is a goemetri random variable. Denoting the number of attempts to suessfully lear the RACH proedure as N A, the expeted number of attempts E[N A ] an be obtained as: E[N A ] = 1 P S = i:e[υ i]<n i:e[υ i]<n E[A i ] E[A i ] E[C i ]. 8 2 Mean Aess Delay: The mean aess delay is the mean delay inurred by a devie to suessfully omplete the RACH proedure starting from the time of its ativation. It inludes the bakoff delays beause of EAB failures and the RACH failures. Clearly, the probability that a devie passes the EAB test is P eab. Also, the number of attempts needed to pass the EAB test is a geometri random variable sine eah attempt is independent. Therefore, the mean number of attempts before a devie passes the EAB test is 1 P eab /P eab. But it requires mean number of attempts E[N A ] to sueed in RACH itself as in 8. Let us assume that for eah failed RACH attempt, it takes a time T R to realize there was a ollision and then a bakoff time T B before the devie starts trying to pass EAB test again for attempting RACH. Note that T R is onsidered beause a devie learns about the ollision after not reeiving the RAR message sine we ignore the apture effet. Sine a devie baks off for T eab whenever it fails to pass the EAB test and sine the NA th RACH attempt is a suess, ignoring the small duration between its ativation and the next RACH opportunity that appears, we an obtain the expeted value of the aess delay T AD for a devie as: [ ] 1 Peab T eab E[T AD ] = E[T rah ]+ E[N A ] P eab +[E[N A ] 1E[T R ]+E[T B ]],

7 7 where, T rah is the time for the devie to get the ontention resolution message in the RACH attempt that is suessful. The mean bakoff time after ollision isw/2 sine the bakoff time is uniformly distributed over [,W 1] window. Hene, [ ] 1 Peab T eab E[T AD ] = E[T rah ]+ E[N A ] P eab +[E[N A ] 1E[T R ]+W/2]. 9 3 Energy Per Cyle: Sine our goal is to minimize the enodeb energy onsumption also, we obtain the mean enodeb RACH Slot Number RACH Slot Number energy onsumed per yle in joules denoted by E yl a EAB.7,8 s b EAB.8,.5 s in serving the RACH requests of the IoT devies as: Fig. 2. Analysis and Simulation plots for expeted attempts, suesses and E yl = minn sf,w rar E[S i] j 1Nmax,N rar max56αp rar t ollisions V/S RACH slots o D i:e[υ i ]<N j=1 sm s 1 The inner sum in 1 evaluates the mean energy onsumed to C. Analytial and Simulation Results transmit RAR messages to E[S i ] devies whih are suessful in RACH slot i of the aess yle. This is essentially 6 with r replaed by E[S i ]. The outer sum overs all RACH slots till all the devies are suessful in the yle. B. Analysis of EAB-BF Clearly, to obtain both the QoS P S and E[T AD ] provided by EAB-BF and the mean energy per yle E yl, the terms E[A i ],E[S i ] ande[c i ] need to be omputed. We next analyze EAB-BF to obtain losed form expressions for these quantities. With the notations defined earlier, we have the following results: Claim 1. The expeted number of devies that make RACH attempt preamble transmission in slot i is given by the following expression: E[A i ] = Q P eab 1 P eab j j= E[F i jq ]+ i jq+1 l=i jq+ W rp Qq +1 i Q+1q, Q Z +,q T eab r p. 11 Proof. The proof is shown in Appendix A. We now turn our attention to the expeted number of ollisions E[C i ]. Claim 2. The expeted number of devies that ollide in slot i an be approximated by the following expression: E[C i ] = E[A i ] E[A i ] 1 1 E[Ai] K Expeted No. of Devies Exp Att Analysis Exp Att Simulation Exp Su Analysis Exp Su Simulation Exp Coll Analysis Exp Coll Simulation Expeted No. of Devies Exp Att Analysis Exp Att Simulation Exp Su Analysis Exp Su Simulation Exp Coll Analysis Exp Coll Simulation We now verify the auray of our analytial expressions using Monte Carlo simulations that average over 5 samples, i.e., 5 aess yles. The simulation ode is written in MATLAB. A total of N = 3 devies are present in the ell. The ativation times of these devies is set to follow the beta distribution as speified by 3GPP [2] and given by 1. Values of α = 3 and β = 4 are onsidered as provided in [2]. Also, T A is assumed to be 1 s. The RACH parameters are set aording to [2, Table ]. The bakoff window is set to 2 ms that is uniformly distributed, so E[T B ] = 1 ms. The RAR Response window size is 5 ms. Sine we do not onsider the apture effet, any devie whih does not reeive the RAR response in at most 5 ms duration after transmitting a preamble onludes its preamble has ollided and deides to bak off. So E[T R ] = 5 ms 6. The ontention resolution message window is uniformly distributed over 48 ms interval. Hene, E[T rah ] = 24 ms. r p E[C l ] PRACH onfiguration index is 6, i.e., r p = 5 ms. ; W We run the simulation for EAB.8,.5s along with the three 3GPP proposed settings during standardization. We show the plots for the expeted number of devies that attempt, sueed and ollide in eah RACH slot for EAB.7,8s and EAB.8,.5s as shown in figures 2a and 2b. It an be seen that the analysis and the simulation plots math very well verifying the auray of our analytial model and validating the approximations that were done. We also tabulate the values for suess probability P S and mean aess delay E[T AD ] for suessful RACH ompletion in Table IV for all the settings. The analysis and simulation values are seen to math well again. Proof. The proof is shown in Appendix B. It will be shown that the approximations made to obtain a losed form expression for E[C i ] are valid and yield aurate results. The evolution of the system is now ompletely expressed in terms of expeted values given by 11 and 12. These are iterative equations, i.e., starting with E[A 1 ] = P eab E[F 1 ] sine P eab is known and E[F i ] an be obtained from 2 we an obtain E[C 1 ]. Then we an find E[A 2 ] by using E[C 1 ] along with E[F 2 ] whih in turn helps to obtain E[C 2 ] and so on. V. JOINT OPTIMIZATION OF EAB-BF AND ENODEB ENERGY CONSUMPTION FOR ENERGY EFFICIENT OPTIMAL PERFORMANCE We now use our validated analytial model to investigate the optimal performane of EAB-BF jointly with respet to enodeb energy onsumption. The following notations are 6 Note that if we had onsidered the apture effet, the devie would learn of its ollision after the Contention Resolution window. Then E[T R ] would beome 25 ms resulting in negligible hanges to the results obtained without apture effet.

8 8 TABLE IV COMPARISON OF ANALYSIS AND SIMULATION RESULTS. SIMULATION RESULTS ARE SHOWN IN BRACKETS P S E[T AD] EAB.5, 16 s s 19.1 s EAB.7, 8 s s 4.7 s EAB.9, 4 s s 3.55 s EAB.8,.5 s s 6.46 s used. Let Peab,T eab denote the optimal setting of EAB- BF that minimizes the mean enodeb energy onsumption per yle E yl under the onstraint that the suess probabilityp S is greater than some threshold and mean aess delay E[T AD ] is less than some threshold T max. We denote E yl ahieved at Peab,T eab as Emin, P S as PS max and E[T AD ] as T min AD objetives:. This investigation helps us ahieve the following i To show how our analytial expressions an be used to build searh algorithms to obtain Peab,T eab settings. These settings an be used by network operators to guarantee the desired QoS to IoT devies with minimal enodeb energy onsumption if EAB-BF is employed. ii To show that the optimal performane of EAB-BF is better than EAB-BB, through results obtained from one example searh algorithm presented. iii To show that the settings that 3GPP onsidered for EAB-BF during standardization proess not only result in suboptimal performane but result in exessive enodeb energy onsumption. iii To make orretions to sub-optimal 3GPP settings that result in substantial gains in the performane. To ahieve the above objetives, we first formulate a onstrained optimization problem. Next, we present an example searh algorithm that makes use of our analytial expressions and some approximations to obtain the near-optimal settings whih are denoted as Peab, T eab to distinguish from the optimal Peab,T eab settings. Even though the mean energy onsumed per yle E yl is a funtion of the variables W, r p, P eab and T eab, our interest urrently lies only in the way P eab and T eab affet the performane of EAB-BF. Hene, we hoose to minimize with respet to P eab and T eab under the onstraint of a lower bound on the suess probability P S and an upper bound on the mean aess delay E[T AD ]. Hene, the optimization is formulated as follows: the objetive E yl min P eab,t eab s.t. E yl P S,E[T AD ] T max P eab,p S, [,1] W,r p,t eab Z +, 13 where, is the lower bound on the suess probability, T max the upper bound on the mean aess delay andw, r p are expressed in milliseonds and T eab in seonds. The objetive E yl is given by 1. To present an example searh algorithm to obtain optimal settings, we make the following observations. Note that E[S i ] = E[A i ] E[C i ] and therefore, the objetive in 13 is non linear in P eab and T eab. Also, with P eab [,1] R and T eab Z +, this formulation belongs to the lass of Mixed Integer Non Linear Programming problems MINLP whih are in general known to be hard to solve theoretially [24]. Usually, some form of single-tree and multi-tree searh methods are applied for solving MINLP problems. For onvex MINLP, hybrid methods that ombine the strengths of singletree and multi-tree searh methods are used. But to lassify the objetive and/or the feasible region as onvex in 13, T eab needs to be relaxed to a ontinuum-valued variable. But that would makee[a i ] on whihe[s i ] depends inomputable by 11 sinet eab appears in the disrete summation. Therefore, the objetive and/or the feasible region annot be approximated as onvex [25]. MoreoverE[A i ], on whih the objetive funtion depends, is multi-modal in nature as shown in Fig.?? for i = 5,15 as P eab and T eab are varied. Even for a fixed i, the behavior of E[A i ] is not easy to haraterize mathematially. The fat that E[C i ] is a non linear funtion of E[A i ] as seen in 12 adds to the diffiulty. For the lass of nononvex MINLP problems, branh-andbound BB also alled spatial BB sbb is one of the well-known methods [24]. But the BB algorithm requires i a proedure to ompute a lower bound on the optimal objetive funtion value of a subproblem and ii a proedure for partitioning the feasible set of a subproblem. But even if we sample P eab and T eab and attempt enumeration in our formulation, the requirements of the BB algorithm annot be satisfied beause of the way E[A i ] depends on P eab and T eab. Beause of the reasons mentioned above, we present an algorithm that employs exhaustive searh. To this end, we evaluate the objetive at only finite sampled set of P eab and T eab values. We then searh for the ombination P eab,t eab that results in the minimum mean energy onsumption E min while satisfying the onstraint of and T max. The values of the objetive obtained at eah sampled P eab,t eab ombination are aurate sine they are omputed using exat equations 1, 11 and 12 that have been derived. Sine we have exat equations for E yl along with P S and E[T AD ] as derived in previous setions, the searh is made simple and does not enounter any onvergene issues that optimization algorithms usually fae. Therefore, if the set of P eab,t eab ombinations that have been sampled ontains the minimizer of the objetive, the solution is guaranteed to be optimal. On the other hand, if the set misses the minimizer of the objetive funtion, then the solution obtained is near-optimal. This is only due to sampling at lesser resolution and not due to any fault in the method per se. Hene, the solution is at Peab, T eab worst near-optimal and denoted by. Note that at Peab, T eab, the suess probability denoted by PS max is the maximum that is possible and the mean delay denoted by T min AD is the minimum that is possible. Our example algorithm to searh for Peab, T eab that yields E min, PS max and T min AD under the onstraint of and T max is shown in Algorithm 1. The algorithm alulates P S, E[T AD ] and E yl for eah sampled pair P eab,t eab in

9 9 TABLE V OPTIMIZING THE PERFORMANCE OF EAB-BF FOR VARIOUS LOWER BOUNDS ON SUCCESS PROBABILITY T min AD P max S E min Peab, T eab T min AD P max S E min Peab, T eab s KJ.17,.1 s s KJ.16,.2 s s KJ.17,.1 s s KJ.13,.2 s s KJ.17,.1 s s KJ.15,.3 s s KJ.17,.1 s s KJ.8,.2 s s KJ.17,.1 s s KJ.22,.8 s s KJ.17,.1 s s KJ.22, 1.1 s s KJ.16,.1 s s KJ.12,.8 s s KJ.14,.1 s s KJ.6,.6 s s KJ.12,.1 s s KJ.9, 1.8 s s KJ.19,.2 s s KJ.9, 1.8 s the for loop between line 4 and 11. Within the for loop, for eah P eab,t eab, the while loop from line 7 to 9 evaluates E[A i ], E[S i ], E[C i ], E[Υ i ] and E yl for eah RACH slot i using the losed form expressions obtained from our analysis. The Energy Consumption Minimizer proedure then searhes for the near-optimal pair Peab, T eab that results in E min for the onstraints and T max. The values of P S and E[T AD ] obtained at Peab, T eab are then PS max and T min AD respetively. A. Comparison with EAB-BB We now ompare the performane of EAB-BF obtained through our analysis with EAB-BB as provided in [9] for N=3 7. To do that, we implement our searh algorithm in MATLAB. P eab is sampled in steps of.1 from to 1, T eab is taken from 1 ms to 2 s in steps of 1 ms. The settings of other parameters are same as onsidered in Setion IV-C for simulations that onform with 3GPP settings and the values used in [9]. is varied from to 1 in steps of.1. T max is set to 5 seonds. We set P o = 17 W, P t =.8 W and δ =.3 as used in [12]. We tabulate the results in Table V for only a subset of values due to spae onstraints. The set of 3-tuples obtained through this searh provide the trade off in EAB-BF performane. Eah 3- tuple indiates the near-optimal ombination of P S, E[T AD ] and E yl that an be ahieved simultaneously when EAB-BF is employed. For omparison with EAB-BB, we onsider only the set of near-optimal 2-tuples PS max,t min AD. We ompare these results with the suess probability and mean aess delay pairs P S,D that are obtainable through EAB-BB mehanism using various ombinations of transmission period of SIB14 T S and the paging yle T P, as shown through Fig. 6a and Fig. 6 in [9]. For EAB-BF, from Table V, it an be observed that the mean P max S,T min AD,Emin delay T min AD reahes.6 and remains within 5 s till P max stays within 2 s till the suess probability Pmax S reahes a value of.8. But for EAB-BB, the mean delay D inreases almost monotonially to more than 5 s before the suess probability P S reahes.5 and is almost 14 s at P S =.9 for EAB-BB as shown through Fig. 6a and Fig. 6 in [9]. Clearly, the mean aess delay obtainable for EAB-BF is lesser than that of 7 We hoose N=3 sine the ase of 3 devies with beta arrivals is onsidered the most severe, leading to RAN overload in a LTE-A ell. S Algorithm 1 To find E min, T min AD, Pmax S, P eab, T eab 1: Initialize step sizes P eab, T eab,. 2: Initialize N, r p, W, K, E[T rah ], E[T R], E[T B], T max. 3: proedure PERFORMANCE EVALUATOR 4: for P eab = : P eab : 1 do 5: for T eab =.1 : T eab : 2 do 6: Initialize E[Υ ],E yl P eab,t eab =, i = 1, q = T eab rp. 7: while E[Υ i] < N do 8: Set Q = i and evaluate: q i jq+1 Q E[A i] = P eab 1 P eab j E[Fi jq] + E[B l ] j= l=i jq+ rp W E[C i] = E[A i] E[Ai ] 1 K E[S i] = E[A i] E[C i] E[Υ i] = E[Υ i 1] + E[S i] minn sf,wrar E = 1 3 mine[si] j 1Nrar max P o +,Nrar max 56 αp t 2D j=1 sm s E yl P eab,t eab = E yl P eab,t eab + E i = i + 1 9: end while E[C i] i:e[υ i ]<N P SP eab,t eab = 1 E[A ; E[NA] = 1 i] P S i:e[υ i ]<N t v = 1 P eabt eab E[N A] P eab + E[T rah ] E[T AD]P eab,t eab = t v + E[N A] 1E[T R] + E[T B] 1: end for 11: end for 12: end proedure 13: proedure ENERGY CONSUMPTION MINIMIZER 14: Find E min s.t P S, E[T AD] T max 15: Find Peab, T eab for whih E yl = E min 16: Set PS max = P S and T min AD = E[T AD] at 17: end proedure Peab, T eab EAB-BB for the same suess probability that an be ahieved in both shemes. The mean aess delay is only 1.46 s for the same suess probability of.9 for EAB-BF proving its superiority over EAB-BB.

10 1 Suess Probability Point C Point B Obtainable EAB.5,16s EAB.7,8s EAB.9,4s Energy in KJ Obtainable EAB.5,16s EAB.7,8s EAB.9,4s Point B Point C Point A Delay in Se Obtainable EAB.5,16s EAB.7,8s EAB.9,4s Point C Point B Point A a Maximum Suess Probability P max S b Minimum Energy Consumption E min Minimum Mean Aess Delay T min AD Perentage Gain Point B Against EAB.5,16s Against EAB.7,8s Against EAB.9,4s Point C Perentage Gain Point B Point A Point C Against EAB.5,16s Against EAB.7,8s Against EAB.9,4s Perentage Gain Point B Point A Against EAB.5,16s Against EAB.7,8s Against EAB.9,4s Point C d Gain in Suess Probability e Gain in Energy Consumption f Gain in Mean Aess Delay Fig. 3. Tradeoff and Gain Curves for maximum suess probability PS max, minimum energy onsumption E min, and minimum aess delay T min AD TABLE VI ENERGY CONSUMPTION PER CYCLE FOR 3GPP SETTINGS EAB Setting EAB.5, 16 s EAB.7, 8 s EAB.9, 4 s Mean Energy Consumed Per yle 3.13 KJ 1.95 KJ.93 KJ B. Trade off Curves and Corretions to 3GPP Settings The plots for PS max, E min and T min AD obtainable from EAB-BF as obtained by our analysis in Table V against the set of lower bounds on are shown in Fig. 3a, Fig. 3b and Fig. 3 respetively. These figures also show the performanes that the three 3GPP settings see tables IV and VI for the 3GPP performanes an provide. Note that the performanes of 3GPP settings are shown as straight lines to indiate that their performane do not depend on the desired. Figures 3d, 3e and 3f show the gains in suess probability, energy onsumption and mean aess delay, respetively, that the near-optimal settings an provide against these three 3GPP settings. It an be seen from these figures that the energy onsumption and the aess delay an be redued by upto 5% with more than 5% gain in suess probability ompared to EAB.9, 4 s. In fat, all the obtainable near-optimal 3-tuples always perform better than EAB.9,4s till touhes about.7 indiated by Point A in figures 3b, 3, 3e and 3f. Beyond Point A, EAB.9, 4 s starts performing better than any optimal 3-tuples and the other two 3GPP settings in terms of energy onsumption and aess delay, but its suess probability is always the worst. A redution of 5% in energy onsumption and around 2% in aess delay against EAB.7,8s an be obtained without degrading the suess probability indiated by Point B in all plots in Fig. 3. Similarly, a redution of 5% in energy onsumption and more than 5% in aess delay against EAB.5, 16 s an be obtained without degrading the suess probability indiated by Point C in all plots in Fig. 3. Hene, the 3GPP settings an be orreted by using the near-optimal barring parameter pairs Peab, T eab that provide these gains and an be obtained from Table V. VI. CONCLUSION 3GPP proposed Extended Aess Barring EAB as the baseline solution to mitigate the RAN overload due to synhronized Random Aess Channel RACH attempts by IoT devies in LTE-A. It was suggested to announe the EAB information either through a barring fator EAB-BF or a barring bitmap EAB-BB. EAB-BB was adopted by 3GPP. In this work, we developed a novel analytial model to obtain the performane metris of EAB-BF. Our analysis results were validated through simulations. Furthermore, we also developed the enodeb energy onsumption model to serve the IoT RACH requests in a LTE-A ell. Our analytial expressions along with the energy onsumption model of the enodeb help to build searh algorithms to obtain EAB-BF settings that an simultaneously minimize enodeb energy